ANSWER
84.30°
EXPLANATION
By the angle addition theorem, the measure of angle RST is,
[tex]m\angle RST=m\angle RSU+m\angle UST[/tex]
Substitute the known values or expressions,
[tex]13x+5=78+3x-12[/tex]
To find the measure of angle RST we have to find the value of x first. Add like terms on the right side of the equation,
[tex]\begin{gathered} 13x+5=(78-12)+3x \\ \\ 13x+5=66+3x \end{gathered}[/tex]
Subtract 3x and 5 from both sides,
[tex]\begin{gathered} 13x-3x+5-5=66-5+3x-3x \\ \\ 10x=61 \end{gathered}[/tex]
And divide both sides by 10,
[tex]\begin{gathered} \frac{10x}{10}=\frac{61}{10} \\ \\ x=6.1 \end{gathered}[/tex]
Now, knowing the value of x, we can substitute this value into the expression for the measure of angle RST,
[tex]m\angle RST=13x+5=13\cdot6.1+5=79.30+5=84.30[/tex]
Hence, the measure of angle RST is 84.30°, rounded to the nearest hundredth.
